Brand new to Blender. Should I download 2.79 or 2.8 beta?
Blender 2.80 is a beta version, under heavy development (there are still 1121 bugs as I'm writing: https://developer.blender.org/maniphest/project/2/type/Bug/). It is a major version, with a lot of changes in the workflow.

Therefore, as of now, 2.79 is more suitable for projects as it has more documentation and is way more stable.

If you are simply willing to explorer Blender, to learn it, and are ready to accept random crashes or occasional unexpected behaviour, you can go for 2.80.

If you are also new to CG, you should go for 2.79 but have a play with 2.80 to get ready for a future transition.